Chapter 14

Chapter 14 Main Principles
Section 14.1 – Introduction to Radical Expressions
	Key Terms:
1.	The number c is a square root of a if  .
2.	The principal square root is the positive square root.
3.	The symbol   is called a radical symbol.
In the expression  , 17 is called the radicand.

Section 14.2 – Multiplying and Simplifying with Radical Expressions.
	Key Terms:
1.	For any nonnegative radicands A and B,  .
2.	The product of square roots is the square root of the product of the radicands.
3.	The square-root radical expression is simplified when its radicand has no factors that are perfect squares.
To take the square root of an even power, take half the exponent.

Section 14.3 – Quotients Involving Radical Expressions
	Key Terms:
1.	The statement   states that the quotient of two square roots is the square root of the quotient of the radicands.
2.	The statement   states that we can take the square roots of the numerator and the denominator separately.
3.	When we find an equivalent expression without a radical in the denominator, we are rationalizing the denominator.
To rationalize a denominator, we can multiply by 1 under the radical to make the denominator of the radicand a perfect square.

Section 14.4 – Addition, Subtraction, and More Multiplication
	Key Terms:
1.	Like radicals have the same radicands.
2.	Expressions such as   and   are known as conjugates.
Learning Objective A: Add or subtract with radical notation, using the distributive laws to simplify.
Section 14.5 – Radical Equations
	Key Terms:
1.	A radical equation has variables in one or more radicands.
2.	The principle of squaring states that if a = b is true, then   is true.
Learning Objective A: Solve radical equations with one or two radical terms isolated, using the principle of squaring once.

Section 14.6 – Applications with Right Triangles
	Key Terms:
1.	A right triangle is a triangle with a   angle.
2.	In a right triangle, the longest side is called the hypotenuse.
3.	In a right triangle, the sides forming the right angle are called the legs.
4.	The equation   is called the Pythagorean equation.
Learning Objective A: Given Lengths of any two sides of a right triangle, find the length of the third side.